In this paper, we introduce a family of harmonic parabolic starlike functions of complex order in the unit disc and coefficient bounds, distortion bounds, extreme points, convolution conditions and convex combination are determined for functions in this family. Further results on integral transforms are discussed. Consequently, many of our results are either extensions or new approaches to thos...

In 1999, for (0≤k<∞), the concept of conic domain by defining k-uniform convex functions were introduced Kanas and Wisniowska then in 2000, they defined related k-starlike denoted k−UCV k−ST respectively. Motivated their studies, our work, we define class k-parabolic starlike functions, k−SHm,q, using quasi-subordination m-fold symmetric analytic making use Ωk. We determine coefficient bound...

To obtain the main result of present paper we use technique differential subordination. As special cases our result, sufficient conditions for $f\in\mathcal A$ to be $\phi-$like, starlike and close-to-convex in a parabolic region.

In this paper, we introduce some new subclasses of analytic functions related to starlike, convex, close-to-convex and quasi-convex functions defined by using a generalized operator and the differential subordination principle. Inclusion relationships for these subclasses are established. Moreover, we introduce some integral-preserving properties. Key-Words: Starlike function; Convex function; ...

in this paper we introduce and investigate a certain subclass of univalentfunctions which are analytic in the unit disk u.such results as coecientinequalities. the results presented here would provide extensions of those givenin earlier works.

This article considers three types of analytic functions based on their infinite product representation. The radius the k-parabolic starlikeness these classes is studied. optimal parameter values for starlike are determined in unit disk. Several examples provided that include special such as Bessel, Struve, Lommel, and q-Bessel functions.

The aim of this paper is two-fold. First, to give a direct proof for the already established result of Styer which states that a univalent geometrically starlike function f is a univalent annular starlike function if f is bounded. Second, to show that the boundedness condition of f is necessary, thus disproving a conjecture of Styer.

are classes of starlike and strongly starlike functions of order β (0 < β ≤ 1), respectively. Note that S∗(β)⊂ S∗ for 0< β< 1 and S∗(1)= S∗ [5]. Kanas [2] introduced the subclass R̄δ(β) of function f ∈ S as the following. Definition 1.1. For δ ≥ 0, β ∈ (0,1], a function f normalized by (1.1) belongs to R̄δ(β) if, for z ∈D−{0} and Dδf(z)≠ 0, the following holds: ∣∣∣arg z ( Dδf(z) )′ Dδf(z) ∣∣∣≤ βπ...

In a recent paper [2], G. R. Blakley raised a question about the decomposition of a ^-valent starlike function into the product of two ^-valent starlike functions. It is the purpose of this note to prove the conjecture of Blakley. Definition 1. The function/(z), regular in |z| <1, is said to be in the class S(p, m), where p and m are positive integers with p^m, if and only if (1) there exists a...